Refer to the Journal of Civil Engineering and Construction Technology (Feb. 2013) study of bottom ash waste asphalt, Exercise 10.15. Recall that the researchers investigated the relationship between the cracking rate y of bottom ash waste asphalt and stress intensity x on data collected for 15 asphalt slabs. In Exercise 10.15 you fit the straight line model relating natural log of crack growth rate to natural log of stress intensity, i.e., ln (y) = β_o + β₁ln(x) + ∈. For this model, conduct a residual analysis that will provide insight into the validity of the standard regression assumptions on the random error, ∈. Do you recommend any model modifications?

Data from Exercise 10.15

A common byproduct of burning municipal solid waste is bottom ash. The use of bottom ash waste in the building of asphalt roads was investigated in the Journal of Civil Engineering and Construction Technology (Feb. 2013). Of particular interest was the relationship between the cracking rate of bottom ash waste asphalt and stress intensity. A mixture of bottom ash waste asphalt was prepared and 15 slabs produced. Stress intensity (number of load cycle applications per millimeter) was varied for each slab, then the cracking growth rate (millimeters per cycle) was measured. 

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ВОTASH Slab Stress Crack Rate 1 0.05 0.004 0.10 0.304 0.15 0.016 4 0.20 0.150 5 0.25 0.116 0.30 0.098 7 0.35 0.008 8. 0.40 0.044 9. 0.45 0.551 10 0.50 1.283 11 0.55 0.365 12 0.60 0.080 13 0.65 9.161 14 0.70 0.097 15 0.75 1.711 2. 3.